"Nicola O." wrote

I've got a wet bathroom wall, tiled surround, outside wall. I've
pulled off some of the tile and backer board and the studs are also
wet/damp to different degrees, worst around the nails which were so
corroded they practically crumbled. There is roll-style insulation
with foil backing-- I can see by poking around the edges of it, that
the insulation is blackened and the outside wall has some black on it
too.
The studs don't appear to be badly rotted but it is softened. It's
worst around the nail holes, soft and black.

Not good, heard of worse though.

So if I pull out the insulation, spray down the walls with bleach, let
dry, then replace everything, does that seem adequate? Is there a
good test of how wet is "too" wet?

No, sorry but until you find out how the water is getting back there, it's
not done. Being an exterior wall, it could even be from the roof. If
there's a window on that wall, could be there. Not enough info here to know
if the shower line runs through that wall as well but if so, thats another
point of possible water.

You need to first stop the water from getting in there, then dry it
completely and have that wood checked. It's fairly simple to sister a stud
if it's not badly damaged yet. (That means to add another stud along side).

Ignored, you will lose the wall and floor. Can happen pretty quick too.